Question bank/NEET UG/Physics

NEET UGPhysicsModerateNEET 2025

There are two inclined surfaces of equal length (ll) and same angle of inclination 45° with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction (μk\mu_k) between the object and the rough surface is close to

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Sol. trough=2tsmootht_{\text{rough}} = 2t_{\text{smooth}}

asmooth=gsin⁡θa_{\text{smooth}} = g\sin\theta

t∝1a⇒tsmooth∝1gsin⁡θt \propto \frac{1}{\sqrt{a}} \Rightarrow t_{\text{smooth}} \propto \frac{1}{\sqrt{g\sin\theta}}

arough=gsin⁡θ−μkgcos⁡θa_{\text{rough}} = g\sin\theta - \mu_k g\cos\theta

troughtsmooth=sin⁡θsin⁡θ−μkcos⁡θ=2\frac{t_{\text{rough}}}{t_{\text{smooth}}} = \frac{\sqrt{\sin\theta}}{\sqrt{\sin\theta - \mu_k \cos\theta}} = 2

Squaring both sides

Source: geekyrakshit/indian-exam-questions / neet2025-code45

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